Question

Are the possible rational roots for the polynomial
x^3-7x^2-x+7=0 numbers 1, -1, and 7?

Answer 1

http://www.purplemath.com/modules/rtnlroot.htm

Answer 2

\(P = {\pm1, \pm7}\)
\(Q = {\pm 1}\)

\(\dfrac{P}{Q} = -1, 1, -7, 7\)

Answer 3

Using those numbers, I got that the resulting quadratic function is (x+1)(x^2-8x+7)=0
Would that mean that by factoring or using the quadratic formula that the final 2 roots would be ±1 and 7? I used quadratic formula and factoring

Answer 4

What do you need to use the quadratic formula for?
\(x^2 -8x + 7\) is factorable

Answer 5

to check my answers. when i factored that I got 1 and 7, would those be the final 2 roots?

Answer 6

When you factor that you should get
\((x + 1)(x - 7)(x - 1) = 0\)

Answer 7

That's how to properly express the factors of the original polynomial. From there it is obvious that the roots are -1, 1, and 7

Answer 8

thank you so much! :) could you help me figure out which possible root produces a remainder of 0 in the function x^4+x^3-6x^2-14x-12=0

Answer 9

For the possible roots I got ±1, ±2, ±3, ±4, ±6, ±12 but i keep getting all numbers except for 0

Answer 10

Make sure you test the negative numbers as well

Answer 11

If you program your calculator properly, you can easily test each number.

Answer 12

Try f(-2)

Answer 13

Then try f(3)

Answer 14

Once again, programming your calculator makes your life much easier

Answer 15

I found those zeroes in less than a minute

Answer 16

how do you program the calculator?

Answer 17

What kind of calculator do you have?

Answer 18

I'm hoping ti-nspire

Answer 19

TI-83 I believe but I've never learned how to do all that

Answer 20

But if not, you can still figure out how to sto a function

Answer 21

or TI-84, one or the other

Answer 22

http://www.youtube.com/watch?v=tRHus5WJveQ

Answer 23

This is why computer programming is so popular. You can learn how solve math problems or computational problems FASTER

Answer 24

Thanks @Hero ! :) I found that -2 produces a remainder of 0 in the function x^4+x^3-6x^2-14x-12=0. But I am confused by the next question, the next question for the same problem is "Now write the resulting cubic function and use synthetic division to find a second root that will reduce the cubic expression to a quadratic expression." How would I go about this?

Answer 25

Good luck with that